The present invention relates to a measuring system for measuring a transfer function matrix of a system to be controlled in a multi-degree of freedom vibration test or vibration control on a test object excited by multiple number of vibrators of a vibration testing apparatus.
In general, in this multi-degree of freedom vibration control, transfer function matrix of a system to be controlled must be determined in advance of the test. The measurements of each element of the transfer function matrix can roughly be classified into the following groups.
{circle around (1)} Classification by excitation methods:
An individual excitation method: a method in which vibrators are each individually excited to measure a column elements of the transfer function matrix; and
A simultaneous excitation method: a method in which vibrators are all simultaneously excited to measure all the elements of the transfer function matrix at once.
{circle around (2)} Classification by excitation signals:
Random signals; and
Sine-wave signals.
Of these classifications, the simultaneous excitation method using the random signals and the individual excitation method using random signals or sine-wave signals have been used hitherto to measure the transfer function matrix, but the simultaneous excitation method using sine-wave signals has never been used.
When comparison is made among the measurements of the transfer function matrix by the known methods on measuring time and a matter of protection of the vibration testing apparatus, the following evaluation is given.
{circle around (1)} Measuring time:
The measurement of the transfer function matrix which is performed in advance of the actual test should preferably be made in minimal measuring time, in consideration of the influence over a test object and the operating time for the test. The individual excitation method in which vibrators are each individually excited to measure the transfer function matrix is lack of practical utility in that the more the vibrators increases, the more time it takes. When comparison on the measuring time for the transfer function matrix is made between the measurement using random signals and the measurement using sine-wave signals, the measurement using random signals generally needs a shorter measuring time.
{circle around (2)} The matter of protection of the vibration testing apparatus:
In the individual excitation method, no consideration can be taken of the influence on other vibrators caused by an operation of one vibrator, for the reason of which the vibration testing apparatus may possibly be damaged. On the other hand, in the simultaneous excitation method, the vibration signals of the vibrators can be adjusted to take consideration of the influences on the mutual vibrators so that possible damage to the vibration testing apparatus is to be avoided. For example, when a test object 53 is simultaneously excited by two vibrators 51, 52, as shown in FIG. 8, the excitation can be adjusted so that the angle xcex8 of the test object 53 not to exceed a predetermined angle limitation.
In consideration of the measuring time and the matter of protection of the vibration testing apparatus, the simultaneous excitation method using random signals can generally be said to be the best method of the known measuring methods and is widely in practical use.
A brief description is given here on the method of measuring the transfer function matrix by means of the simultaneous excitation using random signals.
As shown in FIG. 9, an input signal waveform vector to a system to be controlled (comprising of each signal for driving each vibrator) is denoted as {x} and an output signal waveform vector from the system to be controlled (comprising of each response signal at each control point) is denoted as {y}.
The relation among {X}, {Y} and H is expressed by the following equation (1):
H{X}={Y}xe2x80x83xe2x80x83(1)
where {X} is an input signal spectral vector which is the converted input signal vector in the frequency-domain by use of FFT (Fast Fourier Transformation) or equivalent; {Y} is an output signal spectral vector; and H is a transfer function matrix of the system to be controlled.
When both sides of the equation (1) are multiplied by the transposed vector of the complex conjugate of the vector {X}, the following equation (2) is obtained.
xe2x80x83H{X}{{overscore (X)}}T={Y}{{overscore (X)}}Txe2x80x83xe2x80x83(2)
The left side of the equation (2) is the auto-spectrum matrix of the input signal and the right side thereof is the cross-spectrum matrix between the input signal and the output signal. When these are expressed as Sxx and Sxy, the equation (2) can be rewritten as the following equation (3).
HSxx=Sxyxe2x80x83xe2x80x83(4)
Thus, the transfer function matrix H can be expressed by the following equation (4).
H=SxySxe2x88x921xxxe2x80x83xe2x80x83(4)
where Sxe2x88x921xx is the inverse matrix of Sxx.
In the equation (4), the existence of the inverse matrix Sxe2x88x921xx is required to calculate the transfer function matrix H, and as such requires that Sxx be a regular matrix.
Supposing that the components of the input signal vector are random signals having no correlation, averaging of Sxx allows the components having no correlation other than diagonal components to approach zero in the averaged Sxx, and thus the averaged Sxx results in a diagonal matrix. Since a diagonal matrix is a regular matrix, the existence of the inverse matrix is ensured.
Likewise, averaging process of Sxy allows the components having no correlation between the input signals and the output signals to approach zero in the averaged Sxy, and thus influences from other input signals can be eliminated from the relation between the specific input signals and the response signals.
Thus, the measurement of the transfer function matrix by means of the simultaneous excitation using random signals can be obtained by applying random signals having no correlation to the vibrators to excite the vibrators two or more times, followed by averaging the results.
Incidentally, a sine-wave vibration test that sine-wave excitations are simultaneously applied from the vibrators is sometimes conducted as a multi-degree of freedom vibration test. In this sine-wave vibration test as well, the transfer function matrix of a system to be controlled had to be measured hitherto by using random signals excitation which is different in nature from those in the vibration state in the actual test, that is done by the sine-wave excitation. As a result of this, an adequate accuracy sometimes could not be obtained. This can often be revealed particularly in a system to be controlled such as employing hydraulic actuators having strong nonlinear characteristics.
In the vibration test that uses the information of the transfer function matrix of the system to be controlled, the controllability and thus the test performance is dependent on the accuracy of the measured transfer function matrix of the system to be controlled. Because of this, it is generally preferable for improvement of the test performance to measure the transfer function matrix in the same vibration condition as in the actual test. In view of this, when a multi-degree of freedom vibration test is conducted for the system to be controlled having a strong nonlinear characteristic, it is preferable that the transfer function matrix is measured by use of the same nature signal as in the test, i.e., sine-wave signal, in the same vibration condition as in the test, i.e., in the simultaneous vibration.
When the transfer function matrix is measured with multiple number of vibrators excited simultaneously, influences from other input signals must be eliminated for judgment of the effect on a response point from a specified vibrator. However, in the case of the excitation signals being sine-wave signals, it is difficult to do so, because sine-wave signals themselves are correlative signals. It is the existing situation that the measurement of the transfer function matrix of the system to be controlled in the simultaneous excitation method using sine-wave signals is not practiced even in today""s state of art.
After having conducted devoted researches, the inventors have newly developed the method that when multiple number of vibrators are excited simultaneously, the effect exerted on a response point from a specified vibrator can be judged by shifting phases of the sine-wave signals for driving the vibrators randomly, as in the case of random signals being used as excitation signals. It is the object of the invention to provide a measuring system for a transfer function matrix of a system to be controlled in multi-degree of freedom vibration control which enables the transfer function matrix to be measured with adequate accuracy, based on this method.
To accomplish the above object, the present invention provides a measuring system for measuring a transfer function matrix of a system to be controlled by simultaneous excitation using sine-wave signals prior to a vibration test on a test object is conducted by use of multiple number of vibrators, the measuring system comprising a sine-wave signal generating part in which when the sine-wave signals for driving multiple number of vibrators are generated, the phases between the sine-wave signals are randomly shifted; at least one sensor for acquiring response signal at a response point when multiple number of vibrators are simultaneously excited under the sine-wave signals generated in the sine-wave signal generating part; a spectrum calculating part for calculating an auto-spectrum and a cross-spectrum for one calculation from the spectral data on a vibration frequency obtained from an analysis of the sine-wave signals(i.e., excitation signals) and the response signals acquired by sensors; a spectrum storing part in which the auto-spectrum and the cross-spectrum calculated in the spectrum calculating part are stored in sequence; an arithmetic mean processing part in which the auto-spectra and the cross-spectra for two or more calculations stored in sequence in the spectrum storing part are each arithmetically averaged to find a mean value of the auto-spectra and a mean value of the cross-spectra; a transfer function matrix calculating part in which a transfer function matrix at a specific frequency is calculated from the mean value of the auto-spectra and the mean value of the cross-spectra as found in the arithmetic mean processing part; and a transfer function matrix data storing part in which the transfer function matrix data at specific frequencies calculated in the transfer function calculating part are stored in sequence, to calculate the transfer function matrix at all frequency components.
In the measurement of the transfer function matrix of the system to be controlled by means of the simultaneous excitation using sine-wave signals prior to the vibration test on the test object being conducted by use of multiple number of vibrators, the following steps are taken. First, when sine-wave signals for driving multiple number of vibrators are generated, the phases between the sine-wave signals are randomly shifted and then multiple number of vibrators are simultaneously excited under the generated sine-wave signals. Then, the auto-spectrum and the cross-spectrum for one calculation are calculated from the spectral data on the vibration frequency obtained from the analysis of the excitation signals and the response signals acquired during the excitation. These steps are repeated two or more times to calculate the auto-spectra and cross-spectra for two or more calculations, followed by arithmetically averaging them to find a mean value of the auto-spectra and a mean value of the cross-spectra. Then, the transfer function matrix at a specific frequency is calculated from the both mean values. The foregoing steps are repeated at each frequency to calculate the transfer function matrix at all frequency components.
The discussion is given here on the significance of the random phase shift of the sine-wave signals. In the known method of measuring the transfer function by simultaneous excitation using random signals, the conversion of random signals from time-domain data into frequency-domain data via the Fourier transformation means that the time-domain data is resolved into the sine-wave signals of two or more frequencies. This means that random signals having no correlation with each other randomly vary in phase on a frequency domain at certain spectral components (frequencies). Thus, the random shift of the phases of sine-wave signals can be considered as an extraction of specific spectral component of the random signals having no correlation.
It is understood from this consideration that in the inventive simultaneous excitation method using sine-wave signals as well, the transfer function matrix can be measured on the same principle as in the simultaneous excitation method using random signals. However, in the simultaneous excitation using random signals, the frequency components over the entire range of frequencies can be handled at one excitation, while on the other hand, in the inventive simultaneous excitation method using sine-wave signals, the transfer function matrix at only a particular frequency component can be measured at one excitation, and as such need repeat the excitation at each of the frequencies, to measure the transfer function matrix at all frequency components. From this point, the inventive simultaneous excitation method using sine-wave signals is effective for the measurements in which the transfer function matrix of the system to be controlled need be measured with adequate accuracy prior to the multi-degree of freedom vibration test using sine waves.